Method of reducing effects of a rough sea surface on seismic data

ABSTRACT

A method of correcting seismic data for the effects of a rough sea surface is disclosed. Corrections for the effect of a rough sea surface are made by determining the time-dependent height of the sea surface, either by direct measurement or by calculation from the seismic data. A deconvolution operator is generated from the measured or calculated height of the sea surface and is used to reduce or eliminate the effects of the rough sea surface. Once the data has been corrected for the effect of the rough sea surface, it can be processed in any way suitable for processing seismic data obtained in flat sea conditions.

FIELD OF THE INVENTION

The present invention relates to the field of reducing the effects ofsurface ghost reflections in seismic data obtained in a fluid medium. Inparticular, the invention relates to a method of correcting for theeffects of a rough sea surface on marine seismic data.

BACKGROUND OF THE INVENTION

FIG. 1 is a schematic diagram showing reflections between a sea surface(S), sea floor (W) and a target reflector (T). Various events that willbe recorded in the seismogram are shown and are labelled according tothe series of interfaces they are reflected at. The stars indicate theseismic source and the arrowheads indicate the direction of propagationat the receiver. Events ending with ‘S’ were last reflected at the roughsea surface and are called receiver ghost events. Down-going sea-surfaceghost reflections are an undesirable source of contamination, obscuringthe interpretation of the desired up-going reflections from the earth'ssub-surface.

Removing the ghost reflections from seismic data is for manyexperimental configurations equivalent to up/down wavefield separationof the recorded data. In such configurations the down-going part of thewavefield represents the ghost and the up-going wavefield represents thedesired signal.

Ghost reflections from the sea surface will occur in all sea conditions.Rough seas are a further source of noise in seismic data. Aside from theoften-observed swell noise, further errors are introduced into thereflection events by ghost reflection and scattering from the rough seasurface. The rough sea perturbed ghost events introduce errors that aresignificant for time-lapse seismic surveying and the reliableacquisition of repeatable data for stratigraphic inversion.

The effect of the rough sea is to perturb the amplitude and arrival timeof the sea surface reflection ghost and add a scattering coda, or tail,to the ghost impulse. The impulse response can be calculated by finitedifference or Kirchhoff methods (for example) from a scattering surfacewhich represents statistically typical rough sea surfaces. For example,a directional form of the Pierson-Moskowitz spectrum described byPierson, W. J. and Moskowitz, L., 1964 ‘A proposed Spectral Form forFully Developed Wind Seas Based on the Similarity Theory of S. A.Kitaigorodskii’ J. Geo. Res., 69, 24, 5181-5190, (hereinafter “Piersonand Moskowitz (1964)”), and Hasselmann, D. E., Dunckel, M. and Ewing, J.A., 1980 ‘Directional Wave Spectra Observed During JONSWAP 1973’, J.Phys. Oceanography, v10, 1264-1280, (hereinafter “Hasselmann et al,(1980)”). Both the wind's speed and direction define the spectra. TheSignificant Wave Height (“SWH”) is the subjective peak to trough waveamplitude, and is about equal to 4 times the RMS wave height. Differentrealisations are obtained by multiplying the 2D surface spectrum byGaussian random numbers.

FIG. 2 shows an example of rough sea impulses along a 400 m 2D line(e.g. streamer) computed under a 2 m SWH 3D rough sea surface. Thestreamer shape affects the details of the impulses, and in this examplethe streamer is straight and horizontal. FIG. 2 shows, from top tobottom: The ghost wavelet (white trough) arrival time, the ghost waveletmaximum amplitude, a section through the rough sea realisation above thestreamer, and the computed rough sea impulses. The black peak is theupward travelling wave, which is unperturbed; the white trough is thesea ghost reflected from the rough sea surface. The latter part of thewavelet at each receiver is the scattering coda from increasingly moredistant parts of the surface. Notice that the amplitude and arrival timeghost perturbations change fairly slowly with offset. The arrival timeperturbations are governed by the dominant wavelengths in the seasurface, which are 100-200 m for 2-4 m SWH seas, and the amplitudeperturbations are governed by the curvature of the sea surface which hasan RMS radius of about 80 m and is fairly independent of sea state. Thediffraction coda appear as quasi-random noise following the ghost pulse.

The rough sea perturbations cause a partial fill and a shift of theghost notch in the frequency domain. (The “ghost notch” is a minimum inthe spectrum caused by destructive interference between the directsignal and the ghost signal). They also add a small ripple to thespectrum, which amounts to 1-2 dB of error for typical sea states. Inthe post stack domain this translates to an error in the signal that isabout −20 dB for a 2 m SWH sea.

FIG. 3 shows an example of how such an error can be significant fortime-lapse surveys. The panel on the top left shows a post-stacktime-migrated synthetic finite difference seismic section. The topmiddle panel shows the same data but after simulating production in theoil reservoir by shifting the oil water contact by 6 m and introducing a6 m partial depletion zone above this. The small difference is justnoticeable on the black leg of the reflection to the right of the faultjust below 2 s two-way travel-time. The panel on the right (top) showsthe difference between these two sections multiplied by a factor of 10.This is the ideal seismic response from the time-lapse anomaly.

The left and middle bottom panels show the same seismic sections, butrough sea perturbations for a 2 m SWH (as described above) have beenadded to the raw data before processing. Note that different rough seaeffects are added to each model to represent the different seas at thetime of acquisition. The difference obtained between the two sections isshown on the bottom right panel (again multiplied by a factor of 10).The errors in the reflector amplitude and phase (caused by the rough seaperturbations) introduce noise of similar amplitude to the true seismictime-lapse response. To a great extent, the true response is masked bythese rough sea perturbations. A method for correcting these types oferror is clearly important in such a case, and with the increasingrequirement for higher quality, low noise-floor data, correction for therough sea ghost becomes necessary even in modest sea states.

Exact filters for up/down separation of multi-component wavefieldmeasurements in Ocean Bottom Cable (OBC) configurations have beenderived by Amundsen and Ikelle, and are described in U.K. PatentApplication Number 9800741.2. A normal incidence approximation to thede-ghosting filters for data acquired at the sea floor was described byBarr, F. J. in U.S. Pat. No. 4,979,150, issued 1990, entitled ‘Systemfor attenuating water-column reflections’, (hereinafter “Barr (1990)”).For all practical purposes, this was previously described by White, J.E., in a 1965 article entitled ‘Seismic waves: radiation, transmissionand attenuation’, McGraw-Hill (hereinafter “White (1965)”). However,these prior art techniques require measurements of both velocity andpressure. Moreover, they do not completely correct the complexreflections from rough sea surfaces, and a satisfactory method foreliminating or reducing the effects of a rough sea surface on seismicdata is required.

SUMMARY OF THE INVENTION

The present invention provides a method of reducing the effects inseismic data of downwardly propagating reflected and/or scatteredseismic energy travelling in a fluid medium, the method comprising thesteps of:

a) obtaining seismic data using a seismic source and a seismic receiverdisposed within the fluid medium;

b) determining the height of at least one portion of the surface of thefluid medium as a function of time; and

c) processing the seismic data using the results of the determination ofthe height of the surface of the fluid medium to correct for variationsin the height of the fluid medium. Thus, the present invention providesa method of correcting for the effects of a rough sea surface on marineseismic data. Moreover, in contrast to the prior art techniquesmentioned above, the invention requires only a measurement of the heightof the sea surface.

The portion of the sea surface of which the height is measured may belocated over the seismic source or over the seismic receiver. The heightof the sea surface may be measured at only a single point above theseismic source, or the height of a region of the sea surface above thesource may be measured. Alternatively, if the receiver is a streamer theheight of the sea surface may be measured at a plurality of points alongthe streamer.

The height of the sea surface may be directly measured, for example bysuitable sensors provided on the seismic source or on the seismicreceiver. Alternatively, the height of the sea surface may be determinedfrom the acquired seismic data.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows examples of simple seismic ray paths for primary events,and ghosts that are last reflected from the rough sea-surface;

FIG. 2 illustrates the potential impact of 3D rough sea surface ghostreflection and scattering on consistency of the seismic data waveform;

FIG. 3 illustrates the potential impact of the rough sea surface ghostperturbation on time-lapse seismic data quality;

FIG. 4 schematically illustrates an example of a data processor that canbe used to carry out preferred embodiments of the invention;

FIG. 5 shows the spread function obtained by measuring the height of thesea surface through a circular aperture;

FIG. 6 shows the residual spread function obtained from the spreadfunction of FIG. 5;

FIG. 7 shows the amplitude of the ghost spectra before and aftercorrection for the rough sea surface above the source according to amethod of the present invention;

FIG. 8 shows the phase of the ghost spectra before and after correctionfor the rough sea surface above the source according to a method of thepresent invention;

FIG. 9 shows the amplitude of the ghost spectra before and aftercorrection for the rough sea surface above the receiver according to amethod of the present invention; and

FIG. 10 shows the phase of the ghost spectra before and after correctionfor the rough sea surface above the receiver according to a method ofthe present invention.

DETAILED DESCRIPTION OF THE INVENTION

In the present invention, the effect of a rough sea surface on theseismic data is corrected for by determining the variations in theheight of a portion of the sea surface as a function of time. Thetime-dependent variations in the height of the portion of the seasurface can be directly measured, or they can be calculated from theseismic data. The measured or calculated variations in the height of theportion of the sea surface are used during processing of the seismicdata to reduce or eliminate the effects of the variations in the heightof the sea surface on the processed data. More formally, a deconvolutionoperator is developed from the time-varying height of the portion of thesea surface and the seismic data is operated on by this operator.

The present invention enables the effects of the rough sea to be removedor at least reduced during the processing of the seismic data. The dataobtained in rough sea conditions is thus converted, to a reasonableapproximation, into data that was effectively acquired in flat seaconditions. Once the effects of the rough sea surface have been removed,the seismic data can be further processed as if it were data that hadbeen acquired in flat sea conditions. The further processing of the dataafter correcting for the rough sea surface effects may include a step ofde-ghosting the data to eliminate the effects of reflections from thesea surface, although this is not always necessary.

It is possible to extrapolate from the measured or calculated heights ofthe sea surface, to estimate the time-dependent shape of the sea surfaceaway from the region of the sea surface where the height measurements orcalculations were obtained. It has been found that this extrapolationprovides useful results up to well over 100 m from the region where theheight measurements were obtained.

Once the time-dependent height of the sea surface has been measured orcalculated and the results have been extrapolated to estimate thetime-dependent height of the sea surface away from the region wheremeasurements or calculations were made, the time-dependent rough searesponse function is calculated from the time-dependent height of thesea surface. This can be done by any suitable method such as, forexample, Kirchoff integration. A deconvolution operator for eliminatingthe effects of the time-dependent height of the sea surface is thencalculated, and is applied to the seismic data to correct for theeffects of the time-dependent height of the sea surface.

In an embodiment in which the height of the sea surface is measureddirectly, the portion of the sea surface of which the height is measuredis preferably located either over the seismic source or over the seismicreceiver. Thus, the height of the sea surf ace is measured at one pointonly or over a small area (if the measured portion is located over theseismic source) or essentially along a line of points (if the measuredportion is located over a streamer). In consequence, the angulardistribution of the measured sea surface will not be correct. It hasbeen found, however, that, although the angular distribution of themeasured sea surface is not correct, it is possible to derive a responsefunction that is sufficiently accurate to enable the errors remainingafter deconvolution to be less than 0.5 dB in amplitude and 3.6° inphase.

If the seismic source is a streamer, the method requires that thestreamer is provided with a plurality of depth sensors distributed alongits length, to allow the height of the sea surface at a plurality ofpoints above the streamer to be determined over time (a streamergenerally remains at a substantially constant height above the sea bed).A conventional streamer is provided with one or more depth sensors, formonitoring the depth of the streamer. These conventional depth sensorsare, however, relatively insensitive, and are intended just to give anindication that the streamer is approximately level and is keeping at aconstant height. The conventional sensors are unable to determine thetime-varying shape of the sea surface with the accuracy required by thepresent invention, for two reasons.

Firstly, the conventional depth sensors on a streamer are too widelyspaced to provide a record of the profile of the sea surface that issufficiently accurate for the method of this embodiment of theinvention. The invention requires that the height of the sea surface ismeasured at lateral intervals of around 5m, to obtain a sufficientlyaccurate measurement of the height of the sea surface (the height of thesea surface is preferably measured within 5 to 10 m of each receiver).In conventional streamers, however, the spacing between adjacent sensorsis much greater than this, being typically 200 m.

Secondly, the depth sensors on a conventional streamer are filtered totoo low a bandwidth to be of use in the present invention. Theconventional depth sensors provided on a streamer are hydrostatic depthsensors, and these can detect frequencies of up to around 0.02 Hz. Thereis then a dead-band in the recorded data between 0.02 Hz to about 3 Hz,which is the lowest detected frequency of hydrophones. However, seasurface waves occupy the frequency band of around 0.05 Hz-0.5 Hz, sothat the depth sensors provided on a conventional streamer areunsuitable for detecting the profile of the sea surface with theaccuracy required to put the present invention into effect.

In order to put into practice an embodiment of the present invention inwhich the height of the sea surface above a streamer is measured, thestreamer must be provided with sensors capable of measuring the heightof the sea surface. Each sensor must be able to measure the height towithin an accuracy of approximately 5-10 cm, and must be sensitive inthe 0.05 Hz-0.5 Hz waveband range. A suitable sensor is a pressuresensor or an acoustic echo depth sensor. The sensors are spaced outalong the length of the streamer, preferably at regular intervals. Inoperation, each sensor measures the height of the sea surface above thesensor either continuously or at discrete intervals, and the results ofthe measurements made by the sensors are transmitted to a computer orother data recorder and are stored for use in the data processing.

As an alternative to making measurements of the height of the seasurface at a plurality of points disposed along a line, for examplealong a line over a streamer, the measurements of the height of the seasurface can be made over a region above the seismic source. This can bethought of as measuring the height of the sea surface through anaperture, with results being obtained only for portion of the seasurface “visible” through the aperture.

If the area of a seismic source is small, and a seismic source may havean area of around only 15 metres square, it may well be sufficient tomeasure the height of the sea surface at only a single point above theseismic source. This can be thought of as measuring the height of thesea surface through a point aperture. When the height of the sea surfaceis measured at only a single point it is still possible to carry out theextrapolation step described above to estimate the time-dependent heightof the sea surface away from the point at which the measurements weremade. Although the estimate is poor in appearance, the deconvolutionoperator derived from the estimate is found to be accurate.

In an embodiment in which the height of a region of the sea surfaceabove the seismic source is measured, the region over which the heightof the sea surface is measured is preferably circular, and also ispreferably centred over the seismic source. This introduces symmetry,and simplifies the processing. In principle, however, apertures havingother shapes could be used. The region over the source in which heightmeasurements are taken preferably has a dimension of the order ofmetres. For example, a circle having a radius of around 7.5 metres canbe used.

Where the height of the sea surface is measured not at a single pointbut through an aperture having finite dimensions, in practice the heightof the sea surface is not measured at every point within the aperture. Atwo-dimensional array of depth sensors is used to measure the height ofthe sea surface at a plurality of points within the aperture, forexample at 6 or 8 points. Provided that the sensors are spaced closelyenough, for example with the distance between adjacent sensors being inthe range of 5-10 m, there is no significant loss of accuracy in thesubsequent processing of the data. As in the example above, each sensormeasures the height of the sea surface at a point above the seismicsource either continuously or at discrete intervals, and the results ofthe measurements made by the sensors are transmitted to a computer orother data recorder and are stored for use in the data processing.

A seismic source is generally suspended from a float. One convenient wayof measuring the height of the sea surface at a point above a seismicsource is to mount a sensor on the float to record the height of thefloat. One suitable sensor for this is a GPS receiver.

If the measurements of the height of the sea surface are made through acircular aperture centred above the seismic source, then this aperturein the x-y domain (assuming that the sea surface extends in thex-direction and the y-direction, with the wave height extending in thez-direction) will become a convolution in kx-ky with a point spreadfunction (PSF) that is a cylindrical Bessel function, as shown in FIG.5. The PSF will obscure much of the fine detail of the sea surfacespectrum, and this is equivalent to saying that the aperture throughwhich the height measurements are made is inadequate to describe fullythe shape of the sea surface. The first zero crossing of the PSF is atabout kB=0.5 radians/meter, where kB is the radial variable of theBessel function. Each sample of wave spectrum will be spread over aregion of radius kB.

The height of the sea surface is measured only for a discrete region ofthe sea surface over the seismic source and, as noted above, this leadsto a loss of resolution in the spectrum. However, according to thepresent invention, the height of the sea surface is measured over time,and this measurement over time provides extra information thatcompensates for the loss of resolution caused by the small aperturethrough which the height data are acquired.

If the recorded height data were filtered so that only one angularfrequency, w, is considered at any one time, the real spectrum shouldthen lie entirely on a circle in the wavenumber domain with a radius kgiven by:

k=c(w)/w  (1)

In equation (1), c(w) is the speed of surface waves having an angularfrequency w.

The PSF will spread each sample on this circle over a nearby regionhaving radius kB. The exact shape of the angular spread function isk-dependent, and has the form of a complete circle at low wavenumbersand has the form of an arc at larger wavenumbers. This corresponds tothe lack of directional information being mainly at long surfacewavelengths.

It is straightforward to deconvolve the radial spreading of a singlefrequency component of the data. The values are simply moved backradially onto the circle having radius k=c(w)/w. This procedure can berepeated for each temporal frequency in the spectrum of the sea surface.The residual spread function for a sample at (kx, ky) is thus the arc ofintersection of a circle having radius k centred on the origin with acircular region of radius kB centred on (kx, ky). An example of theresultant spread function is shown in FIG. 6.

At wavelengths that are very short compared with the dimensions of theaperture through which the height measurements are made, the aperture islarge enough that the direction of the waves is estimated reasonablywell. However, there is very little energy at these short wavelengths.Most of the energy of the surface wave is at wavelengths that are longerthan the dimensions of the aperture through which height measurementsare made, and surface waves having these wavelengths cannot be directlymeasured over a full wavelength. Instead, these waves are estimated fromthe time dependence of the height of the sea surface. This gives a goodestimate of the amplitude of the wave, but a poor estimate of itsdirection. When the waves are reconstructed, this poor estimation of thedirection of long wavelength waves means that the reconstructed wavesurface generally has circular symmetry. Only at the very centre of thereconstructed surface, where the measurements were made, does anylife-like detail appear.

It might initially appear that a reflection response calculated from areconstructed wave surface that has such poor angular resolution wouldhave little if any relation to the true response. The inventors havefound however that it is in fact possible to derive a good reflectionresponse from the reconstructed waveform surface. This is because theamplitude and phase of the waves in the estimated waveform surface arecorrect, because they were derived from height measurements taken overtime. The vertical response at a time t involves an integral over thesurface at a radius t/c (where c is the speed of sound in water), sothat the directional error in the spectrum of the surface waves is lesssignificant. Indeed, if the response were purely linear in the heightthen the response would be exactly correct. The off-vertical responsewill be more sensitive to the directional error in the reconstructedsurface waveform, because the integration wave paths are not circles.However, at typical radiation angles used in seismic exploration theerror is acceptable.

FIGS. 7 to 10 show examples of how effective the method of the presentinvention is in reducing the 95% confidence error-bars on the spectra ofreceiver and source ghosts for seismic data obtained in rough seaconditions. FIG. 7 shows the results of correcting for a rough seasurface by taking height measurements above the source. Trace (a) showsthe amplitude of the ghost spectrum obtained for a rough sea surfacehaving a 2 m SWH, and trace (b) shows the result of correcting trace (a)for the rough sea surface using the method described above. Trace (c)corresponds to trace (a) but was obtained for a rough sea surface havinga 4 m SWH, and trace (d) shows the result of correcting trace (c) forthe rough sea surface using the method described above.

FIG. 8 corresponds to FIG. 7, but shows the effect of correcting for therough sea surface on the phase of the ghost spectrum. Traces (a) and (b)were obtained for a sea having a 2 m SWH and traces (c) and (d) wereobtained for a sea having a 4 m SWH.

FIGS. 9 and 10 show the results of a correction based on taking heightmeasurements above the receiver on the amplitude (FIG. 9) and the phase(FIG. 10) of the ghost spectrum. In each of FIGS. 9 and 10, trace (a)shows data obtained in a sea with a 4 m SWH and trace (b) shows theresult of correcting for the rough sea surface using the methoddescribed above.

In the embodiments described above, the height of the sea surface hasbeen directly measured, by means of suitable depth sensors provided onthe source or on the receiver. In a modification of this embodiment ofthe invention, the height of the sea surface is not measured directlybut is estimated from the acquired seismic data. Although the spectrumof the height of the sea surface lies in the dead band of the seismicdata acquisition system, as noted above, it is nevertheless capturedindirectly. This is because some attributes of the seismic data (suchas, for example, the ghost notch frequency), which vary with time overthe trace, have a low frequency limit which is lower than the lowfrequency limit of the acquired data itself. This occurs because theattributes are not linear functions of the data. For example, if astatistical method is developed for rough sea de-ghosting in which thetime shifts for direct and ghost events are estimated from the data(using prior information on correlations derived from the sea state),these data could be used as the input to the surface reconstruction anddeconvolution method described above.

In the embodiment described above, the steps of measuring or calculatingthe height of a portion of the sea surface, extrapolating to estimatethe height of other portions of the sea surface, calculating thetime-dependent rough sea response, and determining the deconvolutionoperator have been described separately for clarity. In principle,however, it is possible to combine one or more these steps into a singleprocessing stage. For example, the step of calculating thetime-dependent rough sea response could be combined with theextrapolation step.

The method of correcting data obtained with a rough sea surface usingmeasurement of the height of the sea surface can be carried out usingany conventional seismic data processing system. The processing ispreferably performed on a data processor configured to process largeamounts of data. For example, FIG. 4 illustrates one possibleconfiguration for such a data processor. The data processor typicallyconsists of one or more central processing units 350, main memory 352,communications or I/O modules 354, graphics devices 356, a floatingpoint accelerator 358, and mass storage devices such as tapes and discs360.

While preferred embodiments of the invention have been described, thedescriptions and figures are merely illustrative and are not intended tolimit the present invention. For example, the only seismic receiverreferred to in the description of the preferred embodiments of theinvention is a streamer. The invention can however be applied to otherreceivers such as, for example, a vertical receiver array.

What is claimed is:
 1. A method of reducing the effects in seismic dataof downwardly propagating reflected and/or scattered seismic energytravelling in a fluid medium, the method comprising the steps of: a)obtaining seismic data using a seismic source and a seismic receiverdisposed within the fluid medium; b) determining the height of at leastone portion of the surface of the fluid medium as a function of time;and c) processing the seismic data using the results of thedetermination of the height of the surface of the fluid medium tocorrect for variations in the height of the fluid medium.
 2. A method asclaimed in claim 1 wherein step (c) comprises calculating adeconvolution operator from the results of the determination of theheight of the surface of the fluid medium, and applying thedeconvolution operator to the seismic data.
 3. A method as claimed inclaim 2 wherein step (c) comprises calculating the sea surface responsefunction from the time-dependent height of the sea surface, andcalculating the deconvolution operator from the sea surface responsefunction.
 4. A method as claimed in claim 3 and further comprisingestimating the time-dependent height of a further portion of the seasurface from the results of step (b) before calculating the sea surfaceresponse function.
 5. A method as claimed in claim 1 wherein step (b)comprises measuring the height of the at least one portion of thesurface of the fluid medium.
 6. A method as claimed in claim 5 whereinstep (b) comprises measuring the height of the surface of the fluidmedium at one or more points.
 7. A method as claimed in claim 6 whereinthe seismic receiver is a streamer and step (b) comprises measuring theheight of the surface of the fluid medium at a plurality of pointslocated along the length of the streamer.
 8. A method as claimed inclaim 6 wherein step (b) comprises measuring the height of the surfaceof the fluid medium at a single point located along above the seismicsource.
 9. A method as claimed in claim 5 wherein step (b) comprisesmeasuring the height of the surface of the fluid medium over an area ofthe surface of the fluid medium.
 10. A method as claimed in claim 9wherein step (b) comprises measuring the height of the surface of thefluid medium over an area that is substantially circular.
 11. A methodas claimed in claim 10 wherein step (b) comprises measuring the heightof the surface of the fluid medium over an area that is substantiallycentred over the seismic source.
 12. A method as claimed in claim 1wherein step (b) comprises calculating the height of the surface of thefluid medium as a function of time from the seismic data.